1. Field of the Invention
This invention relates to the comparison of proportional to absolute temperature signals to bandgap-based reference signals, and more particularly to reducing errors due to the T+Tln(T) deviation from linearity exhibited by bandgap references.
2. Description of the Related Art
The base-emitter voltage V.sub.be of a forward biased transistor is a linear function of absolute temperature T in degrees Kelvin (.degree.K.), and is known to provide a stable and relatively linear temperature sensor: ##EQU1## where k is Boltzmann's constant, T is the absolute temperature, q is the electron charge, I.sub.c is the collector current, A.sub.e is the emitter area, and J.sub.s is the saturation current density. Proportional to absolute temperature (PTAT) sensors eliminate the dependence on collector current by using the difference .DELTA.V.sub.be between the base emitter voltages V.sub.be1 and V.sub.be2 of two bipolar transistors that are operated at a constant ratio between their emitter current densities to form the PTAT voltage. Emitter current density is conventionally defined as the ratio of the collector current to the emitter size (this ignores the second order base current).
The basic PTAT voltage is given by: ##EQU2## The basic PTAT voltage is amplified so that its sensitivity to changes in absolute temperature, can be calibrated to a desired value, suitably 10 mV/.degree.K., and buffered so that a PTAT voltage can be read out without corrupting the basic PTAT voltage.
Such basic PTAT signals are often used as an indicator of the circuit's temperature. The PTAT signal is compared to a reference signal in order to convert the signal from a voltage representation of temperature to one of degrees, yielding a ratio of a PTAT signal to a reference signal. For example, the PTAT signal, e.g. a voltage, may be converted from analog to digital form by an analog to digital converter (ADC) which provides a digital output signal corresponding to the PTAT signal's percentage of the ADCs full scale analog input.
FIGS. 1A and 1B illustrate such a comparison graphically. In FIG. 1A PTAT and ideal, linear, reference signals in, respectively labelled VPTAT and VREF, are plotted against temperature in degrees Celsius. The result of the comparison is illustrated in FIG. 1B, which plots the ratio of VPTAT to VREF versus temperature. The output of an ADC would, naturally, occupy discrete locations along this line which, like the signal VPTAT, is also proportional to absolute temperature. Additionally, ADCs, which often employ regular equal-sized steps, would provide correspondingly regularly spaced output signals. If the reference or PTAT signal were nonlinear, their ratio would also be nonlinear, and the ADC's regular step sizes would lead to temperature measurement errors. To demonstrate the errors that may occur due to nonlinear bandgap voltages, an uncorrected bandgap voltage and a PTAT voltage are plotted versus temperature in FIG. 2A. The resultant ratio VBG/VPTAT is plotted in FIG. 2B, with the ratio's deviation from linearity exaggerated for illustrative purposes.
Bandgap reference circuits have been developed to provide a stable voltage supply that is insensitive to temperature variations over wide temperature range. These circuit operate on the principle compensating the negative temperature drift of a bipolar transistor's base emitter voltage (V.sub.be) with the positive temperature coefficient of the thermal voltage V.sub.T, which is equal to kT/q. A known negative temperature drift associated with the V.sub.be is first generated. A positive temperature drift due to the thermal voltage is then produced, and scaled and subtracted from the negative temperature drift to obtain a nominally zero temperature dependence. Numerous variations in the bandgap reference circuitry have been designed, and are discussed for example in Grebene, Bipolar and MOS Analog Integrated Circuit Design, John Wiley and Sons, 1984, pages 206 through 209, and in Fink et al, Ed. Electronics Engineer's Handbook, third edition, McGraw Hill Book Company, 1989, pages 8.48 through 8.50.
Although the output of a bandgap voltage cell is ideally independent of temperature, the outputs of uncorrected cells have been found to include a term that varies with T-Tln(T). Such an output deviation may yield a bandgap voltage output (V.sub.bg) which increases from a value of about 1.2408 volts at -50.degree. C. to about 1.244 volts at about 45.degree. C., and then returns to about 1.2408 volts at 150.degree. C. This output deviation is not symmetrical; its peak is skewed about 5.degree. C. below the midpoint of the temperature range.
It is difficult to precisely compensate for the temperature deviation electronically, so simpler approximations have been used. One such circuit, described in U.S. Pat. No. 4,808,908 to Lewis et al. assigned to Analog Devices, Inc., the assignee of the present invention, employs a high thermal coefficient of resistance resistor to produce a voltage which is proportional to T.sup.2. This square law voltage approximately cancels the effect of the temperature deviation. Another compensation circuit is described in U.S. Pat. No. 5,352,973 to Audy, assigned to Analog Device, Inc. This circuit provides precise compensation for the Tln(T) deviations but increases the complexity and cost of the basic bandgap cell.
Although conventional bandgap compensation schemes such as the square law compensation of U.S. Pat. No. 4,808,908 or the T+Tln(T) correction scheme of U.S. Pat. No. 5,352,973 may be employed to reduce PTAT/VBG nonlinearity by counteracting that of VBG, these compensation schemes require added cost and increase the complexity of comparison circuits.